Consider the net of a triangular prism where each unit on the coordinate plane represents five feet. If a can of spray paint covers 25 square feet, how many cans of spray paint are needed to paint the outside of the prism blue?
7 cans
To find the number of cans of spray paint needed to paint the outside of the prism blue, we first need to determine the surface area of the prism.
Since the prism is triangular, it consists of two triangular bases and three rectangular faces.
1. Triangular Bases:
The formula to find the area of a triangle is A = (1/2) * base * height.
In this case, each base of the prism has dimensions of 5 units by 5 units on the coordinate plane, which represents 5 feet by 5 feet.
So, the area of one triangular base is A_base = (1/2) * 5 ft * 5 ft = 12.5 square feet.
Since there are two triangular bases, the total area of the triangular bases is 2 * A_base = 2 * 12.5 square feet = 25 square feet.
2. Rectangular Faces:
The dimensions of the rectangular faces can be calculated using the sides of the triangular base.
In this case, each side of the triangular base is 5 units on the coordinate plane, representing 5 feet.
Therefore, the dimensions of the rectangular faces are 5 units by 5 units by 5 units, which represents 5 feet by 5 feet by 5 feet.
The area of each rectangular face can be calculated by multiplying the length, width, and height:
A_rectangular_face = length * width = 5 ft * 5 ft = 25 square feet.
Since there are three rectangular faces, the total area of the rectangular faces is 3 * A_rectangular_face = 3 * 25 square feet = 75 square feet.
Therefore, the total surface area of the prism is the sum of the areas of the triangular bases and the rectangular faces:
Total surface area = Area of triangular bases + Area of rectangular faces
= 25 square feet + 75 square feet
= 100 square feet.
Given that each can of spray paint covers 25 square feet, we divide the total surface area of the prism by the area covered by each can:
Number of cans needed = Total surface area / Area covered by each can
= 100 square feet / 25 square feet
= 4 cans of spray paint.
Thus, four cans of spray paint are needed to paint the outside of the prism blue.